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KVPY SB/SX Mock Test - 3

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  • Question 1
    1 / -0

    Ten trucks numbered 1 to 10, are carrying packets of sugar. Each packet weighs either 999 gm or 1000 gm and each truck carries only the packets of equal weight. The combined weight of 1 packet selected from the first truck, 2 packets from the second, 4 packets from the third, and so on, and 29 packets from the tenth truck is 1,022,870 gm. The trucks that have the lighter bags are

    Solution

    We can find the answer through options as the sum of weights of packet taken from trucks is 1,022,870 gm and its unit digit is 0. The trucks that have heavier bags have unit digit 0. So, in the trucks that have lighter bags, the sum of weights of bags must have unit digit 0.
    So, according to option D, i.e. truck no. 2, 8.
    Truck 2 has 21 bags and total weight = 21 x 999 gm = 1998 gm
    Truck 8 has 27 bags and total weight = 27 x 999 = 128 x 999 gm = 127,872 gm
    So, the unit digit of the weight contained by trucks 2, 8 together is 0.

     

  • Question 2
    1 / -0

    An envelope has space for at most 3 stamps. If you are given three stamps of denomination 1 and 3 of denomination a, (a > 1), the least positive integer for which there is no stamp value is

    Solution

    So, using 1 stamp of value 1, the stamp value is 1.
    Using 2 stamps of value 2, the stamp value is 2.
    Using 3 stamps of value 1, the stamp value is 3.
    Using stamps of denomination a, the lowest stamp value will be a.
    Now, using 2 stamps 1 of value a and the other of 1, a stamp value of a + 1 is obtained.
    Then, using 3 stamps, 1 of value a and 2 of value 1 each, a stamp value of a + 2 is obtained.
    Then, using 2 stamps of value a each, a stamp value of 2a is achieved.
    Then, using 2 stamps of value a each and 1 of value 1, a stamp value of 2a + 1 is achieved.
    As lowest integer has been asked for, we need not worry about 3a.
    Now, putting a = 2, stamp values of 2, 3, 4, 4 and 5 are obtained.
    Putting a = 3, stamp values of 3, 4, 5, 6 and 7 are achieved.
    Putting a = 4, stamp values of 4, 5, 6, and 9 are achieved.
    However, if a = 4, then using stamps of denomination 1, stamp values of 1, 2 and 3 can be achieved as explained before.
    However, if a = 4, the lowest stamp value of 7 cannot be achieved.
    Thus, the least possible integer for which there is no stamp value is 7.

     

  • Question 3
    1 / -0

    The number of ordered pairs (m, n), where m, n ∈ {1, 2, 3, ......, 50}, such that 6m + 9n is a multiple of 5 is

    Solution

    6m + 9n
    Unit digit of 6m = 6
    Unit digit of 9n will be 9 or 1.
    For multiple of 5, unit digit of 9n must be 9.
    It occurs only when n is odd.
    Therefore, total number of ordered pairs = 50 x 25 = 1250

     

  • Question 4
    1 / -0

    The number of rectangles that can be obtained by joining four of the twelve vertices of a 12-sided regular polygon is:

    Solution

    Number of diagonals passing through the centre = 6
    Number of rectangles = 6C2 = 15

     

  • Question 5
    1 / -0

    Let ω be a cube root of unity not equal to 1. Then, the maximum possible value of |a + bω + cω2|, where a, b, c ∈ {+1, -1}, is

    Solution

    |a + bω + cω2|

    |a - c + (b - c)ω|, for maximum value taking a = 1, c = -1, b = 1

    |a + bω + cω2| = |2 + 2ω| = 2|ω2| = 2

     

  • Question 6
    1 / -0

    The number of integers n with 100 ≤ n ≤ 999 and containing at most two distinct digits is

    Solution

    Total number of integers from "100 to 999" = 999 - 99 = 900

    Total number integers in which all are distinct digits = 668

    So, total number of integers containing at most two distinct digits = 900 - 648 = 252

     

  • Question 7
    1 / -0

    Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is held at a temperature of 100°C, while the other one is kept at 0°C. If the two are brought into contact, then, assuming no heat loss to the environment, the final temperature that they will reach is

    Solution

    Since heat capacity increases with the temperature, the amount of heat transfer △T is more at lower temperature than at higher temperature.
    So, the final temperature will be more than 50oC.

     

  • Question 8
    1 / -0

    The following travelling electromagnetic wave Ex = 0, Ey = E0sin(kx + ωt), Ez = 2E0sin(kx - ωt) is

    Solution

    From the equations of Ey and E2, it is evident that wave is circularly polarised.

     

  • Question 9
    1 / -0

    Which of the following has the highest bond angle?

    Solution

    (1) CH4 bond angle will be 109.5o as it has a tetrahedral molecular geometry with sp3 hybridisation.
    (2) CO2 has a bond angle 180o, with sp hybridisation having linear shape.
    (3) H2O has a bond angle 104.5o. It has sp3 hybridisation. Due to the presence of lone pair - lone pair replusions, bond angle reduces to 104.5o.
    (4) SO2 has sp2 hybridisation with bond angle 120o. It has a bent shape.

    Hence, it is clear that CO2 has the largest bond angle.

     

  • Question 10
    1 / -0

    Assuming ideal behaviour, the enthalpy and volume of mixing of two liquids, respectively are

    Solution

    For ideal solution,

    ΔHmixing = 0. No heat should be absorbed or evolved during mixing. This is because there is no change in magnitude of the attractive forces in the two components present.

    ΔVmixing = 0. No expansion or contraction on mixing. Volume of solution is the sum of volume of components present in solution.\

     

  • Question 11
    1 / -0

    The function of enzymes is to

    Solution

    Enzymes are macro-molecular biological catalysts. They accelerate chemical reactions by lowering activation energy.

     

  • Question 12
    1 / -0

    Which of the following diseases is not sexually transmitted?

    Solution

    Tuberculosis is not a sexually transmitted disease. Tuberculosis bacillus is transmitted through droplets expelled into the air by an infected person during normal breathing, while talking or sneezing, but especially when coughing.

     

  • Question 13
    1 / -0

    Sickle cell anaemia is caused by

    Solution

    Sickle-cell disease is caused by a single point mutation (a missense mutation) in the beta-haemoglobin gene that converts a GAG codon into GUG, which encodes the amino acid valine, rather than glutamic acid.

     

  • Question 14
    1 / -0

    Mitochondria are not associated with which of the following functions?

    Solution

    Protein glycosylation occurs in the ER and Golgi apparatus.

     

  • Question 15
    1 / -0

    Diabetes insipidus is due to

    Solution

    Diabetes insipidus can be caused by low or absent secretion of the water-balance hormone vasopressin from the pituitary gland of the brain, or by a poor kidney response to this chemical messenger, which is also called antidiuretic hormone.

     

  • Question 16
    1 / -0

    A ripe mango, kept with unripe mangoes, causes their ripening. This is due to the release of a gaseous plant hormone called

    Solution

    Ethylene affects fruit-ripening. Normally, when the seeds are mature, ethylene production increases and builds-up within the fruit, resulting in ripening of the fruits.

     

  • Question 17
    1 / -0

    A hormone molecule binds to a specific protein on the plasma membrane inducing a signal. The protein that binds to it is called a/an

    Solution

    A receptor is a protein molecule that receives chemical signals from outside a cell. These generally bind to ligands which are hormones. When such chemical signals bind to a receptor, they cause some form of cellular/tissue response, e.g. a change in the electrical activity of a cell.

     

  • Question 18
    1 / -0

    If the sequence of bases in sense strand of DNA is 5'-GTTCATCG-3', then the sequence of the bases in its RNA transcript would be

    Solution

    The base pairing follows the complementary base pairing rule. During transcription, thymine is replaced by uracil. Hence, adenine is hydrogen bonded to uracil by two hydrogen bonds. Guanine is hydrogen bonded to cytosine by three hydrogen bonds. The two strands are antiparallel.

     

  • Question 19
    1 / -0

    Bacteria can survive by absorbing soluble nutrients via their outer body surface, but animals cannot, because

    Solution

    Bacteria have a large surface area as compared to volume as against animals which have a small surface area to volume ratio. Hence, bacteria can survive by absorbing soluble nutrients via their outer body surface. Materials must be able to reach all parts of a cell quickly, and when volume is too large relative to surface area, diffusion cannot occur at sufficiently high rates to ensure this.

     

  • Question 20
    1 / -0

    If you compare adults of two herbivore species of different sizes, but from the same geographical area, the amount of faeces produced per kg body weight would be

    Solution

    A large gut size should provide more space, enabling a large microbial diversity to settle. Hence, if per kg body weight is seen, faeces will be more in the herbivore of smaller size.

     

  • Question 21
    1 / -0

    A couple went to a doctor and reported that both of them were "carriers" of a particular disorder, their first child was suffering from that disorder and that they were expecting their second child. What is the probability that the new child would be affected by the same disorder?

    Solution

    This is a case of autosomal recessive inheritance: Two unaffected people, who each carries one copy of the mutated gene for an autosomal recessive disorder (carriers), have a 25 percent chance with each pregnancy of having a child affected by the disorder.

     

  • Question 22
    1 / -0

    The fluid part of blood flows in and out of capillaries in tissue to exchange nutrients and waste materials. Under which of the following conditions will fluid flow out from the capillaries into the surrounding tissue?

    Solution

    There are two forces at work in capillaries that determine whether water stays as part of the blood in a blood vessel or if water leaves to become part of the interstitial fluid. When the arterial blood pressure exceeds the osmotic pressure, the fluid flows out of the capillaries.

     

  • Question 23
    1 / -0

    In humans, the composition of a zygote that will develop into a female is

    Solution

    The genetic composition of a normal female is 44 autosomes and 2 X chromosomes. Hence, 44 A + XX is the correct option.

     

  • Question 24
    1 / -0

    In which of the following sets of fractions will you find nucleic acids if you fractionate all the organelles from the cytoplasm of a plant cell?

    Solution

    Nucleic acids are found in the nucleus. In plant cells, DNA is also present in chloroplasts and mitochondria.

     

  • Question 25
    1 / -0

    Circadian rhythm is an endogenously driven cycle for biochemical, physiological and behavioural processes. In humans, the approximate duration of this 'biological clock' is

    Solution

    Research has shown that human internal clock runs on a daily cycle of 24 hours, 11 minutes.

     

  • Question 26
    1 / -0

    As proposed by Watson and Crick in 1953, the original model of DNA is a

    Solution

    According to Watson and Crick, DNA is a double helical structure. The two strands are antiparallel i.e both have opposite polarity.

     

  • Question 27
    1 / -0

    In green leaves, the light and dark reactions occur in

    Solution

    In photosynthesis, the light-dependent reaction takes place on the thylakoid membranes. The inside of the thylakoid membrane is called the lumen and outside the thylakoid membrane is the stroma, where the light-independent reactions take place.

     

  • Question 28
    1 / -0

    Which of the following organs is/are capable of producing fructose in humans?

    Solution

    Seminal vesicles produce fructose. It is used to provide energy for swimming sperm cells.

     

  • Question 29
    1 / -0

    Species that are most effective at colonising new habitats show

    Solution

    Dispersal is when individuals or seeds move from one site to a breeding or growing site. Species that show high dispersal ability are most effective at colonising new habitats.

     

  • Question 30
    1 / -0

    Instead of 3, if 2 bases coded for an amino acid, degeneracy of codons coding for the same amino acid would have

    Solution

    Instead of 3, if 2 bases coded for an amino acid, degeneracy of codons coding for the same amino acid would have increased.

     

  • Question 31
    1 / -0

    The condition varicose veins is swelling of veins, that occurs due to

    Solution

    The condition varicose veins is swelling of veins, that occurs due to loss of elasticity of the muscular layer. Varicose veins occurs when veins aren't functioning properly. Veins have one-way valves that prevent blood from flowing backward. When these valves fail, the blood begins to collect in the veins rather than continuing towards heart. Hence, the nearest answer is option 1.

     

  • Question 32
    1 / -0

    Insectivorous plants that mostly grow on swampy soil use insects as a source of

    Solution

    Insectivorous plants grow in soils that are deficient in nitrogen. In order to meet their nitrogen requirement, these plants prey on insects.

     

  • Question 33
    1 / -0

    Two students are given two different double-stranded DNA molecules of equal lengths. They are asked to denature the DNA molecule by heating. The DNA given to student A has the following composition of bases (A:G:T:C:35:15:35:15) while that given to student B is (A:G:T:C:12:38:12:38). Which of the following statements is true?

    Solution

    DNA molecule given to student A would denature faster than that given to student B. This is because the amounts of A and T are higher in DNA sample of student A. A and T are joined by 2 hydrogen bonds and hence, will break faster.

     

  • Question 34
    1 / -0

    Consider a locus with two alleles, A and a. If the frequency of AA is 0.25, then what will be the frequency of A under Hardy-Weinberg equilibrium?

    Solution

    The Hardy-Weinberg Equation: For a population in genetic equilibrium, p + q = 1.0 (The sum of the frequencies of both alleles is 100%.). Hence, the answer is 0.5.

     

  • Question 35
    1 / -0

    Rodents can distinguish between many different types of odours. The basis for odour discrimination is that

    Solution

    Rodents can distinguish between many different types of odours. This is because they have a small number of odorant receptors that bind to many different odorant molecules.

     

  • Question 36
    1 / -0

    For a human male, what is the probability that all the maternal chromosomes will end up in the same gamete?

    Solution

    Each gamete has 23 chromosomes. Hence, the probability that all the maternal chromosomes will end up in the same gamete is 1/23.

     

  • Question 37
    1 / -0

    Brown fat is specialised adipose tissue with abundant mitochondria and rich blood supply. Brown fat

    Solution

    BAT is thermogenic tissue. When activated, BAT cells take lipids and run them through the mitochondria to generate heat, rather than synthesise ATP.

     

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